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Theorem biorfi 407
Description: A wff is equivalent to its disjunction with falsehood. (Contributed by NM, 23-Mar-1995.)
Hypothesis
Ref Expression
biorfi.1  |-  -.  ph
Assertion
Ref Expression
biorfi  |-  ( ps  <->  ( ps  \/  ph )
)

Proof of Theorem biorfi
StepHypRef Expression
1 biorfi.1 . 2  |-  -.  ph
2 orc 385 . . 3  |-  ( ps 
->  ( ps  \/  ph ) )
3 orel2 383 . . 3  |-  ( -. 
ph  ->  ( ( ps  \/  ph )  ->  ps ) )
42, 3impbid2 204 . 2  |-  ( -. 
ph  ->  ( ps  <->  ( ps  \/  ph ) ) )
51, 4ax-mp 5 1  |-  ( ps  <->  ( ps  \/  ph )
)
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184    \/ wo 368
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-or 370
This theorem is referenced by:  pm4.43  918  dn1  957  thema1a  1580  indifdir  3706  un0  3762  opthprc  4986  imadif  5593  xrsupss  11374  mdegleb  21653  ind1a  26613
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